Developping and exploring the interest of deep learning approaches in the field of multi-omics data

Under the supervision of Blaise Hanczar, Farida Zehraoui and Franck Augé

2024-06-12

Aurélien Beaude

Towards a personalized medicine

Omics data

Precision medicine

Outline

1. Single omics

  • State of the Art
  • AttOmics
  • Results

2. Multi Omics

  • State of the Art
  • CrossAttOmics
  • Results
  • CrossAttOmicsGate

3. Interpretability

  • Counterfactuals
  • GAN
  • Results

4. Conclusions and Perspectives

Single omics

State of the art

Limits

Classical deep learning limits

  • High number of parameters
  • With limited number of examples
  • Risk of overfitting

How to reduce the number of parameters ?

Gene expression impacts patient differently

  • With classical DL, features interactions are learned during training and fixed for inference

How to compute interaction specific to each patient ?

(Self)-Attention mechanism

How to pick relevant information from input data \(X = [x_i]_{1 \leq i \leq L}\) ?

  • Self-attention allows to capture the associated context of each input element by interacting with other elements \[ \operatorname{Attention}\left({\color{query}Q},{\color{key}K},{\color{value}V}\right) = \operatorname{softmax}\left(\frac{{\color{query}Q}{\color{key}K^T}}{\sqrt{d_k}}\right){\color{value}V} \] \(\color{query}Q = \left[q_i\right]_{1 \leq i \leq L}\) with \(\color{query}q_i = X_i \cdot W_q\), \(\color{key}K\) and \(\color{value}V\) are obtained similarly.
  • Quadratic complexity (Space and Time)

How to apply self-attention to large large vectors ?

Group related features together and apply self-attention on it.

AttOmics Architecture

Grouping Strategies

  • Random
  • Clustering
  • Knowledge:
    • Gene ontology
    • Cancer Hallmarks

\[ \begin{align} X_G &= \mathcal{T}\left(X\right) \\ &= \left[X_{g_1}, \cdots, X_{g_4}\right] \end{align} \]

Intra-group interactions

Gene grouping creates unwanted restrictions

Genes in group \(g_1\) cannot interact with genes from other groups

Restore group interactions with the Attention mechanism.

\[ X'_{g_i} = \operatorname{FCN}\left(X_{g_i}\right) \]

\[ X'_G = \left[X'_{g_1}, \cdots, X'_{g_4}\right] \]

Inter-groups interactions

New representation of each group taking into consideration features from other groups

\[ \begin{align} \color{query}q_i &= \color{query}X'_{g_i} \cdot W_q^h \\ \color{key}k_i &= \color{key}X'_{g_i} \cdot W_k^h \\ \color{value}v_i &=\color{value} X'_{g_i} \cdot W_v^h \end{align} \]

\[ \begin{align} Z &= \operatorname{MultiHeadAttention}\left(X'_G\right) \\ &= \operatorname{concat}\left(\left[h_1, \cdots, h_H \right]\right) \\ h_i &= \operatorname{Attention}\left({\color{query}Q},{\color{key}K},{\color{value}V}\right) \end{align} \]

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Results

Cancer Signature

  • Cancer heatmaps are a mean of patient heatmaps with the same cancer
  • Each square of the heatmap represents the attention weight between two different group learnt by the model

Across cancers different interactions are learnt

CESC cancer

Identified pathways:

  • IL6 JAK STAT3 signaling
  • Hedgehog signaling
  • WNT singaling

Identified interactions:

  • WNT and Hedgehog cross-talk involved in chemo-resistant cervical cancer

AttOmics Conclusions

  • Proposed a grouping mechanism to scale the self-attention to omics data
  • AttOmics has less parameters and achieves similar or better performances
  • AttOmics has better performances with a limited training set
  • Self-attention: capture patient specific feature interactions

Omics were analyzed individually but a phenotype results from their interaction

Combine the different omics in a single model.

Multi omics

Multimodal AI

State of the art

Attention as an integration strategy

Attention mechansim can capture interaction between two vectors

Early Fusion

  • High dimensionnality
  • Attention complexity: \(\mathcal{O}(n^2)\)

Intermediate Fusion

 

 

\[\begin{align} Z_{\beta \rightarrow \alpha} &= \operatorname{CrossAtt}_{\beta \rightarrow \alpha}\left(X_{\alpha}, X_{\beta} \right) \\ &= \operatorname{Attention}\left(Q_{\alpha},K_{\beta},V_{\beta} \right) \end{align}\]

Consider all modality pairs: \(n^2\) pairs to consider

Only consider pairs known to interact

CrossAttOmics

Omics combination

Identifying important interactions

Layer-wise relevance propagation

Robustness to missing modalities

Multi-omics conclusions

  • Harness cross-attention to build a multimodal representation explicitly considering interactions between modalities.
  • Using only two or three non-protein omics combination, achieve similar accuracy to what is obtained by training only on proteins.
  • Modality dropout increases robustness to missing modalities.
  • Data-driven strategy to identify important interactions: CrossAttOmicsGate.

Patient can be diagnosed efficiently but what are the disease drivers? How to treat the patient?

From predictions to actions

Motivation

What are the important genes or potential biomarkers?

Whate are the actions that could lead a patient to a healthier state?

Counterfactuals

Counterfactuals

How would \(x\) change if \(y\) had been \(y^{\prime}\)?

\(y\) was predicted because input \(x\) had values \(\left(x_{1}, x_{2}, x_{3}, \ldots\right)\). If \(x\) instead had values \(x_{1}^{\prime}\) and \(x_{2}^{\prime}\) while other variables, \(\left(x_{3}, \ldots\right)\), had remain the same, \(y^{\prime}\) would have been predicted.

(Wachter et al., 2017)

\[ \operatorname*{argmin}_{x^{\text{CF}}} \mathcal{L}\left(g\left(x^{\text{CF}}\right), y^{\text{CF}} \right) + d\left(x^{\text{CF}}, x\right) \]

Is it sufficient to have realistic and actionnable points?

Counterfactuals properties

Data manifold closeness = respect the original data distribution

GANs captures the data distribution (Goodfellow et al., 2014)

Generating counterfactuals with a GAN

\[ \mathcal{L} = {\color{manifold}\mathbb{E}_{x\sim p_{d}}\left[ D\left(x\right)\right] - \mathbb{E}_{x^{\text{CF}}\sim p_{g}}\left[ D\left(x^{\text{CF}}\right)\right] + \lambda \mathbb{E}_{\tilde{x}\sim p_{g}}\left[ {\left( {\left\|\nabla_{\tilde{x}}D\left(\tilde{x}\right) \right\|}_{2} -1 \right)}^{2}\right]} \\ + {\color{cf}\mathcal{L}_{\operatorname{Cl}} + \mathcal{L}_{\operatorname{Cl}_{T}}} + {\color{sparsity}\mathcal{L}_{\text{Reg}}\left(G\right)} \]

Preliminary Results

  • Counterfactual Accuracy (\(y^{\text{CF}}\) ✅︎ and \(y_{\text{Tissue}}\) ✅︎): \(\mathcal{A}_{\text{CF}} = 0.96\)
  • Distance to the original point: \(L_1\), \(L_2\), \(L_{\infty}\)
  • Sparsity: \(L_0 = \sum_i \left|x_i \right|^{0}\) with \(\left|0\right|^0 = 0\)
  • kNN Accuracy: \(\mathcal{A}_{\text{kNN}} = \frac{1}{k} = \sum_{i=1}^{k} \mathbb{1}\left(y^{\text{CF}}, y_{i}^{\text{kNN}}\right)\)

\(L_1\) 2440
\(L_2\) 30
\(L_{\infty}\) 1
\(L_0\) 0.52
\(\mathcal{A}_{\text{kNN}}\) 0
\(\mathcal{A}_{\text{Oracle}}\) 0.94

Preliminary Results

Preliminary Results

GDA: gene-disease association from DisGenet / COSMIC: Catalogue of somatic mutations in cancer

Conclusions and Perspectives

Conclusions

  • AttOmics: Applied self-attention mechanism to omics profile tp capture patient-specific interactions. Self-attention was applied to groups of features which allowed the addition of knowledge in the groups.
  • CrossAttOmics: Integrate multi-omics data based on the known regulatory interactions between modalities and the cross-attention.
  • CrossAttOmicsGate: Let the network score each interaction with a gating mechanism
  • Counterfactual Generation: Find the perturbation on the molecular profile that will change the prediction from a disease state to a health

Perspectives: Scalar Attention

  • Groups are an architectural constraints
  • Directly consider feature interactions

How to compute attention between scalar values ?

\[ A_{ij} = \operatorname{softmin}\left(\left|Q_{i} - K_{j} \right| \right) \]

Efficient implementation with Triton.

Perspectives: Knowledge

  • Biolgically-informed architectures are common when applying deep learning to biological problems as they provide a strong inductive bias.

Knowledge is incomplete or may contains errors. How to handle this ?

Knowledge is iteratively constructed and omics measurement represent a mean of all occuring pathwyays.

What to do about unnannotated features ?

Thank you

Appendix

CrossAttOmicsGate: a data-driven approach

CrossAttOmicsGate results

Model Accuracy Precision Recall F1
No Gate 0.980 ± 0.001 0.982 ± 0.002 0.979 ± 0.002 0.980 ± 0.002
Gate 0.987 ± 0.001 0.989 ± 0.001 0.987 ± 0.001 0.987 ± 0.001

Adversarial training of \(\operatorname{Cl}\)

  • An adversarial example, \(x^{\star} = x + \delta\), is an instance \(x\) with the addition of a small perturbation \(\delta\) that is incorrectly predicted by a model
  • They are obtained by solving \(\max_{\delta \in \Delta} \mathcal{L}\left(\operatorname{Cl}\left(x + \delta\right), y\right)\) with gradient ascent. (ex: projected gradient ascent)
  • Adversarial training: \[ \min_{\operatorname{Cl}} \mathbb{E}_{(x,y)}\left[\max_{\delta^{\star} \in \Delta} \mathcal{L}_{\text{CE}}\left(\operatorname{Cl}\left(x+\delta^{\star}\right), y \right) \right] \]